Acrylic ink, which I use for love of waterproofness and opacity and so forth, is indeed waterproof.
Evidentally it's not milkproof.
I laid down some treetrunks in acrylic ink and glazed over them with white gouache. They weren't receding as much as I'd like after multiple coats, so I went to the next Big Gun--casein, a milk-based paint that's more opaque than gouache, but still workable for awhile after drying, unlike acrylic.
And I discovered, about a minute afterwards, that the casein picked the pigment right out of the acrylic ink and turned into a tan smear.
Painting was salvaged through hasty paper-towel use, and a little experimentation would indicate that dripping and patting the casein is reasonably safe and delivers the white-over-brown effect I was after, but it was still an interesting discovery. Ultimately a fairly happy accident--the globs and splotches look very bark-like--but kind've a surprise. Water does not equal milk. Who knew?
This is why I don't use oil paints--the notion of linseed oil and turpentine and god knows what toxic solvents would overwhelm my feeble brain. I got a B in AP Chemistry because I always typed my lab reports and wrote clear, lucid prose, not because I ever made any of the experiments work. (I maintain that this is entirely the wrong way to teach kids science, but that's another rant for another day...)